Calabi's unboundedness conjecture for complete minimal hypersurfaces

Let $n\geq 2$, and let $\Sigma^{n}\subset \mathbb{R}^{n+1}$ be a complete minimal hypersurface. Calabi's conjecture. The hypersurface $\Sigma^{n}$ must be unbounded. This is the unboundedness part of the Calabi conjectures for complete minimal hypersurfaces. The paper studies this question in higher dimensions and proves a chord–arc estimate relevant to it; the supplied context does not establish whether the conjecture itself is resolved in all dimensions.